LONDON—News Corp Executive Chairman Rupert Murdoch was secretly recorded playing down the significance of wrongdoing at his U.K. newspapers and criticizing a police investigation as "totally incompetent," remarks that sharply contrast with his public contrition over the papers' alleged use of illegal reporting tactics.

Britain's Channel 4 News and the journalism website Exaro News posted excerpts of the recording online, saying it was made in March during a meeting with journalists at the Sun tabloid, some of...